How many strings of letters from the set {A, B, C} have length 11 and have exactly 4 A's (repeated letters are allowed)? O P(11, 4) x 37 11! 4!-4!-3! O C(11, 4) × 2' O C(11, 4) x 37 O H x 27 O P(11, 4) x 27
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- Implement a commonly used hash table in a program that handles collision using linear probing. Using (K mod 13) as the hash function, store the following elements in the table: {1, 5, 21, 26, 39, 14, 15, 16, 17, 18, 19, 20, 111, 145, 146}. Use c++Implement a commonly used hash table in a program that handles collision using linear probing. Using (K mod 13) as the hash function, store the following elements in the table: {1, 5, 21, 26, 39, 14, 15, 16, 17, 18, 19, 20, 111, 145, 146}.You are given a list of randomly arranged numbers, for example (11,7,18,5,17,13). The triple (11,7, 5) is called the "inversion triple" because (5<7<11) in terms of value, while the index of 5 in the list is greater than the index of 7, and the index of 7 is greater than 11. Therefore, we can find 2 inversions in such list as follows: (11,7,5), and (18,17,13). Your main task is to find the total number of inversions in any given list. a) Design a brute-force algorithm to return the number of possible inversions, and analyse the complexity of your solution b) Develop a python code to implement your brute-force algorithm. [The marks depend on the correctness of the code, indentation, comments, test-case] c) Design a more efficient algorithm to do the same task with less complexity, and analyse the complexity of your solution. [Important instruction to be followed: Create an arbitrary unsorted list of 8 characters and use it to provide full explanation of how your proposed…
- Define the set U = {x ∈ Z | ∃y ∈ Z, xy = 1} = {+1, -1}. We say a number p ∈ Z \ {0} is prime if and only if p ∉ U and ∀a ∈ Z, ∀b ∈ Z, p|ab ⇒ (p|a ∨ p|b). (intuitively this says you can’t build a prime p by combining things which do not already contain p) We say a number i ∈ Z is irreducible if and only if ∀a ∈ Z, ∀b ∈ Z, i = ab ⇒ (a ∈ U ∨ b ∈ U) (intuitively this says p is irreducible if the only things which divide it are 1 and p (and -1, and -p).) Prove that if x = ab ≠ 0 and x|a then b ∈ U.Suppose you generate the following RSA key pairs:• p = 37199• q = 49031• N = p · q = 1823904169• (p − 1) · (q − 1) = 1823817940• e = 65537 (for encryption)• d = 1578812933 (for decrption)Assuming a=01, b=02, . . . , z=26, and we group the digits in groups of three. (ii) If you receive strings of digits from a sender: 199770170, 1288754980, 324346846, 1370682962, decrypt the message.Given the following sets: U= {1,2,3,4,5,6,7,8,}, A={1,4,5,7}, B= {2,5,6,7,}, and C= {3,4,6,7} Complete the following set operations: a. A U(BUC) b. (A N (B N C))' . c. (A N B) U ( A N C) d. (A N B')U (A N C')
- Please answer it in Python Write a function pairsbypairslist that would return pair by pair from the smallest value to the biggest value For example [12, 13, 11, 15], # return : (11, 12) and (13, 15) [9, 15, 4, 24, 19, 2] # return : (2,4) (9,15) (19,24) [1, 5, 9, 15, 21, 9, 12, 9], # return : (1,5) (9,9) (9,12) (15,21)write a program that creates a linked list of points in an x-y coordinate system. Following are the node content of your linked list: head -> P1(0,1) -> P2(1,2) -> P3(10,11) -> P4(0,3) -> P5(17, 16) -> P6(0,0) -> P7(3,4) -> P8(16,1) ->tail Where Pz(x,y) is point z with x and y coordinates in the 2D space. Write a method searchList that recursively searches the linked list of point objects for a specified point w with x1 and y1 cooredinates: Pw(x1, y1). Method searchList should return true if it is found; otherwise, false should be returned. Use your method in a test program that creates the above list. The program should prompt the user for a value to locate in the list. For example: Enter two integer values representing the x and y coordinate of the point you want to look for in the list: 3 4 This point is found Anothet example: Enter two integer values representing the x and y coordinate of the point you want to look for in the list: 0 1 The point does…Let A be the set of all strings of decimal digits of length 5. For example 24157 and05189 are strings in A.(a) How many strings in A have exactly one 7?(b) How many strings in A have at least two 2’s?(c) How many strings in A have the digits in a strictly decreasing order? For example97643 and 54321 are such strings, but 14820 and 95421 are not.
- Which of the following sets is a set partition for the universe U = { 1, 2, 3, 4 } ? 1.P = { { 2, 3, 4 }, { 1, 3, 4 } } 2.P = { { 3, 4 }, { 1, 2 } } 3.P = { { 4 }, { 1, 2 } } 4.P = { { 3, 4 }, { 1, 2, 3 } }Implement the __getitem__ method to work with positive and negative indices. For example: > W = L1(Node(10, Node(20, Node(30)))) > print W [ 10, 20, 30 ] > print W[0], W[1], W[2] > print W[-1], W[-2], W[-3] 10 20 30 30 20 10 Be aware of cases where the index exceeds the size of the list, either positive or negative. In these cases you have to generate an assertion error. In the above example, W[3] and W[-4] should raise an AssertionError Complete the Code: class L(object): def __init__ (self, first_node=None): assert first_node is None or isinstance(first_node,Node), "first must be Node, not %s"%(type(first_node)) self.first_node = first_node def __len__(self): k = self.first_node if k is None: return 0 i=1 while k.next is not None: i+=1 k = k.next return i def __repr__ (self): if self.first_node is None:…Given a singly linked list of integers, reverse the nodes of the linked list 'k' at a time and return its modified list. 'k' is a positive integer and is less than or equal to the length of the linked list. If the number of nodes is not a multiple of 'k,' then left-out nodes, in the end, should be reversed as well.Example :Given this linked list: 1 -> 2 -> 3 -> 4 -> 5 For k = 2, you should return: 2 -> 1 -> 4 -> 3 -> 5 For k = 3, you should return: 3 -> 2 -> 1 -> 5 -> 4 Note :No need to print the list, it has already been taken care. Only return the new head to the list. Input format :The first line contains an Integer 't' which denotes the number of test cases or queries to be run. Then the test cases follow. The first line of each test case or query contains the elements of the singly linked list separated by a single space. The second line of input contains a single integer depicting the value of 'k'. Remember/Consider :While specifying the list…